Polarizing beamsplitters were first described by Mary Banning in "Practical Methods of Making and Using Multilayer Filters", J. Opt. Soc. Amer., Vol. 37, pages 792-797, (1947), who constructed a polarizing beamsplitter by coating successive layers of two different thin-film materials having alternately high and low indices of refraction upon the hypotenuse of a first 45.degree. prism, and by cementing the hypotenuse of an identically dimensioned second 45.degree. prism to the coated hypotenuse of the first prism to form a cube. The refractive index n.sub.0 of the prisms, and the refractive indices n.sub.1 and n.sub.2 of the thin-film materials, were selected by Banning in accordance with Brewster's condition so that the p-component (i.e., the time-varying component of the electric vector parallel to the plane of incidence) of an optical beam incident upon a side of the cube formed by the prisms is transmitted through the successive thin-film layers between the prisms without undergoing substantial deviation at the interfaces between the successive thin-film layers. The thickness of the coating of thin-film layers was selected by Banning so that the s-component (i.e., the time varying component of the electric vector perpendicular to the plane of incidence) of the optical beam incident upon the side of the cube is partially reflected from each of the successive thin-film layers.
When a cube beamsplitter according to Banning's design is positioned in an optical beam in such a way that a side of the cube (i.e., a side of the first prism) is perpendicular to the beam, the beam (after passing through the first prism) is incident upon the interface between the first prism and the first thin-film layer (i.e., upon the hypotenuse of the first prism) at an angle of incidence equal to the prism angle .theta..sub.0, which is specified to be 45.degree.. The relationship between the angle of the beam in the first prism to the angle of the beam in the first thin-film layer is given by Snell's law as: EQU n.sub.0 sin .theta..sub.0 =n.sub.1 sin .theta..sub.1 ( 1)
where .theta..sub.0 and .theta..sub.1 are the angles of the beam in the first prism and in the first thin-film layer, respectively, relative to the normal to the interface between the first prism and the first thin-film layer. The condition for non-deviation of the p-component of the beam in passing from the first thin-film layer into the second thin-film layer is given by Brewster's law as: ##EQU1## where .theta..sub.2 is the angle of the beam in the second thin-film layer relative to the normal to the interface between the first thin-film layer and the second thin-film layer (which is substantially the same as the normal to the interface between the first prism and the first thin-film layer). The angles .theta..sub.1 and .theta..sub.2 are completely independent of the order of the successive thin-film layers coated over the hypotenuse of the first prism, and are also completely independent of the thicknesses of the thin-film layers.
Combining equations (1) and (2) gives the relationship between the refractive indices n.sub.O, n.sub.1 and n.sub.2 as: ##EQU2## as the condition for non-deviation and non-reflection of the p-component of the incident beam in passing through the succession of thin-film layers having alternating high and low indices of refraction n.sub.1 and n.sub.2.
The reflection of the s-component of the incident beam from the successive first and second thin-film layers is greatest when each of the layers has an optical thickness of one-quarter wavelength for the particular wavelength .lambda..sub.0 for which the beamsplitter is designed (typically, a wavelength at the center of the operating range of the system in which the beamsplitter is to be used). Thus, for maximum reflection of the s-component, the thickness d.sub.1 of the first thin-film is given by: ##EQU3## and the thickness d.sub.2 of the second thin-film layer is given by: ##EQU4##
When the conditions set by equations (4) and (5) are satisfied, the reflectivity R.sub.I at the interface between the first and second thin-film layers (regardless of whether the beam is being propagated from the first layer into the second layer, or vice versa) can be derived from Maxwell's equations as: ##EQU5## If the coating of thin-film layers on the hypotenuse of the first prism comprises k successive pairs of layers of materials having refractive indices n.sub.1 and n.sub.2, and a final single layer of the material having refractive index n.sub.1 ; and if every one of the layers in the coating satisfies the conditions set by equations (1) and (2), as appropriate; then any desired amount of reflectivity of the s-component of the incident beam can be achieved by using a sufficient number of pairs of thin-film layers. To a good approximation, the reflectivity of the s-component is given by: ##EQU6## where n.sub.1 &gt;n.sub.2.
In the beamsplitter design of Banning for which the prism angle is 45.degree., the p-component is transmitted through the first prism into and through the successive thin-film layers into the second prism, from which the p-component emerges as a polarized beam collinear with respect to the incident beam. The s-component is transmitted by a beamsplitter according to Banning's design through the first prism into the successive thin-film layers, and is partially reflected from each of the successive thin-film layers back into the first prism so as to emerge from the first prism as a polarized beam having a direction of propagation perpendicular to the incident beam.
In the beamsplitter design of Banning, reflections of the p-component occur at the interface between the first prism and the first thin-film layer of the coating, and at the interface between the final thin-film layer and the second prism. These p-component reflections "contaminate" the reflected s-component. However, for visible wavelengths, the p-component reflections are relatively small and can ordinarily be ignored. For infrared wavelengths, on the other hand, the indices of refraction of the thin-film materials are quite high, and consequently the reflectivity of the p-component is high and the p-component reflections generally cannot be ignored.
In the prior art, the fabrication of a cube beamsplitter for visible wavelengths conventionally involved bonding a surface of a first prism to a surface of a second prism using an optical cement having the same (or approximately the same) index of refraction n.sub.O as the prism material. However, for infrared wavelengths, an optical cement cannot be used in bonding two prisms together, because there are no optical cements presently available that are sufficiently transparent in the infrared region of the electromagnetic spectrum to transmit a p-component of useful intensity from the first prism into the second prism. Furthermore, there are no optical materials readily available at the present time that can be used in combination to satisfy the condition set by equation (3) for non-deviation and non-reflection of the p-component through successive thin-film layers of alternating high and low indices of refraction.